MATHEMATICS

THE SIMPLEST MATHEMATICS
1. On the Simplest Possible Branch of Mathematics
A. MS., n.p., [c.1903?], pp. 1-9, 13, 17-33.
Brief discussion of paradisaical logic, i.e., system of logic in which only one value is supposed, provided another value (or other values) is not positively denied. The simplest kind of mathematics referred to, however, is a two-valued system of which Boole's algebra of logic is regarded as a special case. Inadequacies of Boolean algebra and some merits of secundal notation. Rules and examples for common mathematical operations in CSP's dyadic system.

2. On the Simplest Branch of Mathematics (SM)
A. MS., n.p., [c.1903?], pp. 1-2; 1-5, incomplete, with an alternative p. 5.
The pure mathematics of existential graphs, alpha and beta parts, with definitions and permissions of transformation. See MS. 512 for more of MS. 2.

3. On Dyadics: the Simplest Possible Mathematics (D)
A. MS., n.p., [c.1903?], pp. s-2, incomplete.
Intended as the first of a series of four memoirs, with plans for further memoirs on the application of mathematical theory to deductive logic. The doctrine of multitude and a working definition of "continuity." See MS. 511.

4. Sketch of Dichotomic Mathematics (DM)
A. MS., n.p., [c.1903?], pp. 1-52 (p. 25 missing), with 11 pp. of variants.
Nominal and real definitions; definition of terms, e.g., "postulate," "axiom," "corrollary," "theorem," which are employed in mathematical or geometrical demonstration; canon of demonstration. Long digression which begins with recognition of seven schools of philosophy each determined by the emphasis placed upon one or more of the following concepts: form, matter, and entelechy. The relationship of these schools to the realist-nominalist controversy, with special attention given to the Aristotelian position. The nature of signs: sign and related notions, especially form, law, habit and entelechy; sign as having its being in the power, not act, of determining matter; sign as entelechy.

5. Dichotomic Mathematics (DM)
A. MS., n.p., [c.1903?], pp. 1-4, 1-3, 2-9, 6-11, 6-8, 10, 16-7, 45-46, with 22 pp. belonging to other drafts.
Similar in content to MS. 4, but without any of the digressions.

6. [Dyadic Value System]
A. MS., n.p., n.d., 2 pp.
The simplest of value systems serves as the foundation for mathematics and, indeed, for all reasoning, because the purpose of reasoning is to establish the truth or falsity of our beliefs, and the relationship between truth and falsity is precisely that of a dyadic value system.

7. On the Foundations of Mathematics (Foundations)
A. MS., n.p., [c.1903?], pp. 1-16, with 3 rejected pages; 17-19 of another draft. Mathematics as dealing essentially with signs. The MSS. below (Nos. 8-11) are drafts of this one, and all are concerned with the nature of signs.

8. On the Foundations of Mathematics (Foundations)
A. MS., n.p., [c.1903?], pp. 1-4, 3-4; 4-8 of another draft.

9. [Foundations of Mathematics]
A. MS., n.p. [c.1903?], pp. 1-5, with rejected pages. Vagueness, generality, and singularity.

10. [Foundations of Mathematics]
A. MS., n.p., [c.1903?], pp. 1-2.

11. [Foundations of Mathematics]
A. MS., n.p., [c.1903?], pp. 1-2, incomplete.

12. Notes Preparatory to a Criticism of Bertrand Russell's Principles of Mathematics (B. Russell)
A. MS., n.p., February 5, 1912, pp. 1-14.
The comments on Russell's work are as follows: ". . . true in the main" and "throughout, however, he betrays insufficient reflection on the fundamental conceptions of the subject," with the "primary difficulty . . . his not having begun with a thorough examination of the elements; . . . the ultimate analytic of thought." The major part of the manuscript concerns CSP's own analytic of thought (theory of signs).

13. On the Logic of Quantity (L of Q)
A. MS., n.p., [c.1895], pp. 1-13; 7-12, with an alternative p. 8 of another draft.
The principal questions raised are these: Why mathematics always deals with a system of quantity, what the different systems of quantity are and how they are characterized, and what the logical nature of infinity is. The relationship of logic and metaphysics to the three categories of Firstness, Secondness, and Thirdness. Singular, dual, and plural fasts. Chaldean metaphysics; chaos to determinacy; the evolutionary process. Postulates of mathematical logic (pp. 7-12).

14. On Quantity, with special reference to Collectional and Mathematical Infinity (Quantity)
A. MS., n.p., [c.1895], pp. 1-34.
The nature of mathematics, pure and applied. In general, mathematics is concerned with the substance of hypotheses, drawing necessary conclusions from them; pure mathematics is concerned only with those hypotheses which contain nothing not relevant to the forms of deduction. The nature of quan-tity (real, rational, and imaginary). System of quaternions as an enlargement of the system of imaginary quantity. Possible grades of multitude. Spatial and temporal continuity. Common sense notions of continua, especially with regard to the flow of time. "Continuum" defined as "a whole composed of parts, with the parts of the whole comprising a series, such that, taking any multitude whatever, a collection of those parts can be discovered the multitude of which is greater than the given multitude." Lastly, reasons are given for thinking that continuity exists beyond the evidence afforded by our natural beliefs in the continuity of space and time.

15. On Quantity, with special reference to Collectional and Mathematical Infinity (Quantity)
A. MS., n.p., [c.1895], pp. 1-29, incomplete.
Same questions raised as in MS. 14. "Mathematics" defined, with extended comments on the divisions of the sciences.

16. On the Logic of Quantity, and especially of Infinity (Logic of Quantity)
A. MS, n.p., [c.1895], pp. 1, 5-9, 7-18, 18-20.
Several definitions of "mathematics," including Aristotle's and CSP's. Mathematical proof and probable reasoning; the system and scale of quantity; the importance of quantity for mathematics. But to grasp the nature of mathematics is to grasp the three elements, which, with regard to consciousness, are feeling, consciousness of opposition, and consciousness of the clustering of ideas into sets. Recognition of the three elements in the three kinds of signs logicians employ. An analysis of the syllogism.

17. On the Logic of Quantity (Logic of Quantity)
A. MS., n.p., [c.1895], pp. 1-9; 7-10 of another draft.
This manuscript should be compared with MS. 16, to which it bears a special similarity. See also MS. 250 where CSP defines "mathematics" as "the tracing out of the consequences of an hypothesis." Five definitions of "mathematics." Benjamin Peirce's definition found acceptable with modification. "Science" defined in terms of the activity of scientists, not in terms of its content or "truths." Probable inference and certain features of mathematical proof (pp. 7-10).

18. (Logic of Quantity)
A. MS., n.p., n.d., pp. 3-4.
Defense of a modified version of Benjamin Peirce's definition of "mathematics." Cf. MS. 78.

19. Logic of Quantity (Logic of Quantity)
A. MS., n.p., n.d., pp. 1-12.
Several theorems demonstrated, e.g., that every relation included under a preference is itself a preference. Solution is offered to the following problem: Required that property which a collection must have to prevent it from proceeding from any collection of which it forms a part.

20. Logic of Quantity (Logic of Quantity)
A. MS., n.p., n.d., pp. 1-5; 1-4, 3-5; plus a single-page table of contents ("Contents") and 3 rejected pages.
Definitions, corollaries, theorems, and problems. The theorems and problems differ from those in MS. 19.

21. Memoire sur la Logique de la Quantite. Deuxieme Partie.
A. MS., n.p., n.d.. pp. 1-16, with 5 rejected pages.
The application of the logic of relations to quantity.

22. Systems of Quantity
A. MS., n.p., n.d., 5 pp.
Definitions of "relation," "relationship," "ring-relationship," and "quantity." Systems of logical, collectional, and total quantity distinguished.

23. [Logic of Number]
TS., n.p., n.d., pp. 2-7.
A draft of G-1881-7 (for annotated reprint of, see MS. 38). Unlimited and limited discrete simple quantity.

24. The Theory of Multitude (Multitude)
A. MS., n.p., [c.1903], pp. 1-3; 3-4 of another draft.
"Multitude" defined in terms of collection, followed by a pragmatistic definition of "collection."

25. Multitude and Number (Multitude)
A. MS., G-1897-1, pp. 1-82, with rejected or alternative pages running brokenly from p. 7 to p. 71.
Most of manuscript was published (4.170-226, except 187n1) but omitted were several illustrations (pp. 21-24; 34) and several proofs of theorems, among which are the following: That the collection of possible sets of units which can be taken from discrete collections is always greater than the collection of units (pp. 12-13), that the sum of an enumerable collection of enumerable multitudes is an enumerable multitude (pp. 29-32), and that there is a vast collection of indefinitely divident relations between the units of any denumerable collection (pp. 40-54).

26. On Multitude (On Multitude)
A. MS., n.p., [c.1897], pp. 1-24, with 24 pp. of rejects and/or alternatives.
An inquiry into what grades of multitude of collections are mathematically possible. This is a logical inquiry because both a strict logica utens and the principles of logica docens are required. Collection is explained but not precisely defined. Provided are three axioms relating to collections and several theorems. The inquiry concludes with a discussion of the general method of drawing conclusions by means of the above system.

27. Considerations concerning the Doctrine of Multitude
A. MS., n.p., [c.1905-07?], pp. 1-5; 23, 24, 27, 29, 30.
The nature of definition; "collection" defined; first- and second-intentional collection.

28. [On Multitudes]
A. MS., n.p., [c.1897?], pp. 23-48.
Abnumeral collection; first, second, and third denumeral multitude; princi, secundo, and tertio post-numeral multitude. Continuity and the doctrine of limits.

29. [On Multitudes]
A. MS., n.p., n.d., 10 pp.
Innumerable and inenumerable multitude. Generality and infinity.

30. Note on the Doctrine of Multitude
A. MS., n.p., [November 1903], pp. 1-6; 1-2.
Doctrine of multitude is developed in terms of dog-names and boy-names. See CSP - Josiah Royce correspondence, 11/13/03, and the CSP-E. H. Moore correspondence, 12/16/03.

31. On the theory of Collections and Multitude
A. MS., n.p., [c.1905-07?], 2 pp.; plus 1 p. (p. 2) ("Note on Collections").

32. [On Collections]
A. MS., n.p., n.d., pp. 1-2, incomplete.
"Collection" defined; collection and quota distinguished.

33. [On Collections and Multitudes]
A. MS., n.p., n.d., pp. 4-8.

34. [Collections and the Fermatian Inference]
A. MS., n.p., n.d., 26 pp. of discontinuous fragments (nn. except for 67).

35. [Fermatian Inference]
A. MS., n.p., n.d., 5 pp.

36. [Fragments on Collections]
A. MS., n.p., n.d., 14 pp.

37. On the Number of Forms of Sets
A. MS., n.p., n.d., pp. 1-3.
Explanation of form and formality in terms of plurality and diversity of sets. Table of formalities.

38. On the Logic of Number Reprints, G-1881-7.
One of the two reprints is annotated. Undated revisions in the form of marginal notes.

39. Logic of Number
A. MS., n.p., n.d., 18 pp.
Fundamental premises concerning number.

40. Axioms of Number
A. MS., n.p., [C.1881?], 4 pp.
Fifteen axioms (or assumptions) of arithmetic which provide a definition of "positive, discrete number" and from which, CSP thought, every proposition of the theory of numbers may be deduced by formal logic. Definitions of "addition" and "multiplication."

41. The Axioms of Number
TS., n.p., n.d., 2 pp.

42. [Cardinal and Ordinal Number]
A. MS., n.p., n.d., 10 pp.

43. [Cardinal Number]
A. MS., n.p., n.d., pp. 36-38.
Mathematical calculations on the versos of these pages.

44. First Definition of Ordinals (Topics)
A. MS., G-c.1905-3 [G-1904-3], pp. 26-49, with 10 pp. of rejects and/or alternatives.
Published, in part, as 4.331-340. Omitted: an attempt to define formally a secundal system of enumeration (pp. 38-39) and a second example (pp. 46-49).

*45, [Second Definition of Ordinals]
A. MS., n.p., [1904], pp. 4-6; 19-22; and 1 p. (the number of which is missing).
Parenthetically: "As for the whole existing race of philosophers, say John Dewey, to mention a relatively superior man whom you see, why they are the sort of trash who are puzzled by Achilles and the Tortoise! Think of trying to drive any exact thought through such skulls! Royce is the only philosopher I know of real power of thought now living."

46. [Ordinals]
A. MS., n.p., n.d., pp. 6-7.
Second definition of "ordinals," and first and second ordinal definition of "addition." Also multitudinal definition of "addition."

47. Proof of the Fundamental Proposition of Arithmetic
A. MS., n.p., [1890?], pp. 1-4.
The proposition to be proved: ". . . that the order of sequence in which the things of any collection are counted makes no difference is [in] the result, provided there can be any order of counting in which the count can be completed. "

48. Numeration (Num)
A. MS., n.p., n.d., pp. 1-20, with 44 pp., some of which belong to different drafts but many of which are rejected pages.
Definitions of "number" and "series." The distinction between precise and definite; vague and indefinite. Abstraction, or ens rationis. In what sense can it be said that entia rationis are real? These pages were probably intended for an arithmetic.

49. An Illustration of Dynamics (Illustration)
A. MS., n.p., [c.1901-02?], pp. 1-20, with 3 pp. of variants.
Setting out from two problems of dynamics both of which require for their solution the method of infinitesimals, CSP attempts an explanation of the method of infinitesimals, which requires, in turn, an explanation of collections and multiplicity. In addition, there is a discussion of the different modes of being, followed by a discussion of the distinction between reality and existence (for the purpose of showing that although nothing unreal can exist, something may be non-existent without being unreal).

50. (Attraction)
A. MS., n.p., [c.1901-02?], pp. 1-12, with a rejected p. 10.
Contents are similar to those of previous manuscript, but without the discussions of existence and reality and of collections.

NUMERICAL NOTATION AND ANALYSIS

51. On the Ways of Thinking of Mathematics (W of T)
A. MS., n.p., [c.1901-02?], pp. 1-4, with a rejected p. 3.
On the decimal and secundal systems of enumeration.

52. Notes on Numerical Notation
A. MS., n.p., [c.1910?], pp. 1-10, plus a rejected p. 2.
The notion of "elegance" in mathematics. The secundal system.

53. Secundal Computation
A. MS., n.p., [c.1912?], pp. 1-6, with 2 other attempts to write p. 2.
The notion of "elegance" in mathematics. The secundal system. Modes of reality.

54. Secundal Computation, Rules
A. MS., n.p., [early 1912], 8 pp., with 3 rejected pages; plus 1 folded sheet ("rules for addition and subtraction").
Notational explanation and accompanying statement of the rules for multiplication, division, addition, and subtraction. The extraction of square roots.

55. Computations for a Table of Secundal Antilogarithms
A. MS., n.p., n.d., pp. 2-4.

56. Calculation of I.V.I. and Secundal Expression
A. MS., n.p., n.d., pp. 1-2; plus a folded sheet ("Calc. of Table of Secundal Logarithms").

57. Essay on Secundal Augrim (SA)
A. MS., n.p., [c. February 1905?], pp. 1-9.
Dedicated to James Mills Peirce and concerned with the same material as MS. 54.

58. Secundal Augrim
A. MS., n.p., n.d., 1 p.
Calculation of fundamental antilogs by additive method. Calculation of (10)01.

59. Secundal Augrim. Calculation of 10-01 by additive method continued
A. MS., n.p., n.d., 1 p.

60. Secundal Augrim. Sheet 1
A. MS., n.p., n.d., 1 p.

61. Secundal Numerical Notation (Secundals)
A. MS., n.p., n.d., pp. 1-12, with variant pages 7 and 9.
The four distinguishing characteristics of the system of secundals. CSP's version of the secundal system, with its several rules and examples of their application.

62. [Notes on Secundal Numeration]
A. MS., n.p., [c.1905?], 1 p., with 64 pp. of secundal calculations.

63. [Secundal Notation Employed in Finding Factors]
A. MS., n.p., n.d., 11 pp.

64. Notes for my treatise on Arithmetic
A. MS., notebook, n.p., n.d.
Mostly on secundals. Versos contain calculations pertinent to pendulum experiment, and two of these pages are dated Paris 1876.

65. The Binary Numerical Notation
A. MS., n.p., n.d., pp. 1-2; 1-2 ("The Binary System of Numerical Notation").

66. Mathematics as it is to be treated in my Logic treated as Semiotics
A. MS., n.p., [c.1892-94?], pp. 1-5.
Binary system of notation.

67. Sextal Numeration
A. MS., notebook, n.p., n.d.
Transformation of an integer from decimal or sextal to secundal expression and back again to the decimal expression. Synthemes.

68. Note on a Series of Numbers (Series)
A. MS., n.p., [c.1903?], pp. 1-12, with variants (pp. 7, 8-12).
The series investigated is that whose first two dozen members are 2 S 3 S 3 S 4 S 5 S 5 S 4 S 5 S 7 S 8 S 7 S 7 S 8 S 7 S 5 S 6 S 9 S 11 S 10 S 11 S 13 S 12 S 9 S 9 S

69. Numerical Equations
A. MS., n.p., n.d., 1 folded sheet (2 pp.).
Method of getting all the roots when their moduli are all different.

70. Analysis of some Demonstrations concerning definite Positive Integers (N)
A. MS., G-1905-6, pp. 1-20, with 50 pp. of variants and notes.
See notes for an explanation of existential graphs. The versos of some pages contain notes for dictionary. In addition there is a draft of a letter in reply to an advertisement appearing in the New York Herald.

71. Of the Unordered Combinations of Six Things (6 Things)
A. MS., n.p., [c.1899], pp. 1-8.
The symmetrics of combinations of six things.

72. On the Combinations of Six Things
A. MS., n.p., n.d., 1 p.

73. A Problem of Trees
A. MS., n.p., n.d., 4 pp. (incomplete or unfinished).
The problem for which a solution is offered is to find how many distinct forms there are for a row of a given number of letters (separated into two parts by a punctuation mark, and each part not consisting of a single letter into two parts by a subordinate punctuation mark, and so on until all letters are separated).

*74. On the Number of Dichotomous Divisions: a problem in permutations
A. MS., n.p., n.d., pp. 1-10 (p. 7 missing); plus 17 pp. of another draft.
In the calculus of logic, a proposition is separated by its copula into two parts. The two parts may again be separated in a like manner, and so on indefinitely. One may inquire how many such propositional forms with a given number of copulas there are. Similar problem in algebra.

ALGEBRA

75. Notes on Associative Multiple Algebra
A. MS., n.p., n.d., 23 pp.
"The main proposition of this note was presented to the American Academy of Arts and Sciences, May 11, 1875; and is published in the Proceedings of the Academy on p. 392." It is clear that this manuscript and the following two (76 and 77) belong together. See G-1875-2 and 3.150-151.

76. II. On the Relative Forms of the Algebras
A. MS., n.p., n.d., pp. 1-7.
A draft of G-1881-10 (Addendum 2).

77. III. On the Algebras in which division is unambiguous
A. MS., n.p., n.d., pp. 8-14.
A draft of G-1881-10 (Addendum 3).

78. Notes on B. Peirce's Linear Associative Algebra (LAA)
A. MS., n.p., n.d., pp. 1-5.
A defense of Benjamin Peirce's definition of "mathematics": Six possible objections noted and countered. Cf. G-1881-10 and MS. 18.

79. Nilpotent Algebras
A. MS., n.p., n.d., 1 p.
Double and triple algebras.

80. Nilpotent Algebras
A. MS., n.p., n.d., 3 pp.

81. Notes on the Fundamentals of Algebra
A. MS., n.p., n.d., 2 pp.
Copula. Ligations, both simple and branching.

82. On the Application of Logical Analysis to Multiple Algebra
A. MS., n.p., n.d., pp. 1, 3-4.
See G-1875-2.

83. Index to Jordan's "Substitutions"
A. MS., n.p., n.d., 8 pp.

84. [Algebraical Problems]
A. MS., n.p., n.d., 3 pp.
Drafts of corresponding pages of MS. 165.

85. An Algebraical Excursus
A. MS., n.p., n.d., pp. 1-2.

86. On the Quadratic Equation (QE)
A. MS., n.p., n.d., pp. 1-5.
On the real, equal, or imaginary roots of quadratic equations.

87. Rough Sketch of Suggested Prolegomena to your [i.e., James Mills Peirce's] First Course in Quaternions
A. MS., n.p., [c.1905?], pp. 1-20, 16-19, 17-26, and 20 pp. of variants.
The mathematician's threefold task involves substituting hypotheses for less definite descriptions of real or imaginary states of affairs, then developing a point of view for making those hypotheses as comprehensible as possible, and finally employing that point of view for the purpose of solving problems. Mathematical theory is the discovery of methods of treating a broad class of problems from one general point of view. Quaternions as a particular theory of tridimensional space. Analysis of spatial and temporal relations. Listing Numbers.

88. Quaternions Applied to Probabilities
A. MS., n.p., [1860's, early 1870?] 1 folded sheet (4 pp.).

89. Quaternions Theory of Functions
A. MS., n.p., n.d., 7 pp.

90. [Quaternions]
A. MS., n.p., [c.1876], 2 pp.
Quaternion algebra. Hamilton's and Benjamin Peirce's forms interpreted geometrically.

CALCULUS OF FINITE DIFFERENCES

91. A Treatise on the Calculus of Differences (Calc. Diff.)
A. MS., n.p., [1903-04?], pp. 1-25, with twice as many pages from other drafts.
For "calculus of differences" CSP preferred "calculus of successions." He planned to divide treatise into four parts, but the manuscript only gets into the first part which, treating the subject generally without regard to the na-ture of known quantities, is occupied mainly with equations of differences. The distinction between logical and mathematical functions. Features of mathematical functionality. Definitions of "value," "universe of values." "quantity." Notational rules.

92. Note on the Notation of the Calculus of Finite Differences (NFD)
A. MS., n.p., [1903-04?], pp. 1-4.
The calculus of finite differences and the differential calculus compared, especially with respect to the notion of function.

93. Calculus of Finite Differences
A. MS., n.p., n.d., pp. 1-2, with 2 pp. (of two other starts); 1 p. ("The Logic of Finite Differences"); 3 pp. ("Equations of Finite Differences"); a notebook ("Promiscuous Notes").
The notebook from p. 17 onward is devoted to Boole's Finite Differences and related topics (Tagalog is the major subject of the first part of notebook).

BRANCHES AND FOUNDATIONS OF GEOMETRY

94. New Elements of Geometry by Benjamin Peirce, rewritten by his sons, James Mills Peirce and Charles Sanders Peirce.
A. MS., n.p., n.d., pp. 1-6, 1-4 ("Preface"), 2 pp. ("Nota Bene"), pp. 1-398, (pp. 7, 31-33, 35, 69-70, 74-76, 78, 92-94, 166-168, 175, 182-183, 235 missing), with pp. xvi, xvii, xviii, xix, and pp. 37-150 from Benjamin Peirce's Plane and Solid Geometry mounted and ready for revision.
Rewritten are books II-V concerned with the fundamental properties of space, topology, graphics, metrics.

95. [The Branches of Geometry; Ordinals]
A. MS., notebook, G-1904-3 and sup(1) G-c.1905-3, pp. 1-34.
An address delivered to the National Academy of Sciences. There is no indication of publication under G-1904-3, but this is G-c.1905-3 which is a mistake. see sup(1) G-c.1905-3.

*96. [The Branches of Geometry; Existential Graphs]
A. MS., n.p., [c.1904-05?], 11 pp.

97. [The Branches of Geometry]
A. MS., n.p., n.d., pp. 9-16, with 5 pp. of variants.

98. The Axioms of Geometry
A. MS., n.p., [c.1870-71?], 2 pp., with 3 pp. of other starts.

99. The Axioms of Geometry. Attempt at enumerating them
A. MS., n.p., [c.1875-76], l p.

100. First Attempt at a Geometry Logically Correct
A. MS., notebook, n.p., September 21, 1874.

101. [Six Fundamental Properties of Space]
A. MS., n.p., n.d., 2 pp.
CSP's intention is to explain imaginaries in a new way, bringing them into the orbit of synthetic geometry by means of the principle of continuity.

ANALYTIC GEOMETRY

102. Promptuarium of Analytic Geometry
A. MS., n.p., n.d., 5 pp. and 4 pp. of different drafts.

103. Syllabus of Plane Analytic Geometry
A. MS., n.p., n.d., 5 pp.

104. On Real Curves
A. MS., n.p., n.d., pp. 1-5, with variant p. 4.

105. On Real Curves. First Paper
A. MS., n.p., n.p., n.d., 13 pp.

*106. Four Systems of Coordinates
A. MS., n.p., n.d., 16 pp.

EUCLIDEAN AND NON EUCLIDEAN GEOMETRY

107. Synopsis of Euclid
A. MS., n.p., n.d., 2 pp.

108. [Euclid's Elements; Properties of the Number 2; the Meaning of "Rational"]
A. MS., n.p., n.d., pp. 1-4.

109. Pythagorean Triangles (Pyth. Tri)
A. MS., n.p., [c.1901?], pp. 1-4.

110. Note on Pythagorean Triangles
A. MS., n.p., n.d., 1 p.

111. Formulae for Plane Triangles
A. MS., n.p., n.d., 1 sheet.

112. Notes on Klein Icosahedron
A. MS., n.p., n.d., 12 PP.

*113. Icosahedron (Icosahedron)
A. MS., n.p., n.d., 16 pp.

114. On Hyperbolic Geometry (Hyp. Geom)
A. MS., n.p., [c.1901?], pp. 1-6, 16-20, with rejected pages.
Formulae required for the projection of the hyperbolic plane upon the Euclidean. Definitions of "individual," "independence of individuals," and "collection." Fundamental theorem of multitude. (Cantor's demonstration of this theorem is thought to be fallacious.)

115. Newton's Enumeration of Cubic Curves
A. MS., n.p., n.d., 7 pp.
Hyperbolic geometry.

116. Brocardian Geometry
A. MS., n.p., n.d., 1 p.

117. The Non-Euclidean Geometry made Easy
A. MS., G-undated-7, pp. 1-8.
Published, in part, as 8.97-99. Unpublished (pp. 3-8). Denial of either the first or second of the two "natural propositions," noted in that part of manuscript which was published, leads to a non-Euclidean geometry. Both of the corresponding kinds of non-Euclidean geometry are intelligible, and a consideration of plane geometry will suffice to show this.

118. Reflections on Non-Euclidean Geometry
A. MS., n.p., n.d., pp. 1-5.

119. Non-Euclidean Geometry
A. MS., n.p., [c.1883 or later], 1 p. and 1 p. ("Notes on Non-Euclidean Geometry") .
The purpose of this memoir is to find some way of treating geometry metrically by introducing the absolute synthetically. The attempt is restricted to plane non-Euclidean geometry: "Solid non-Euclidean geometry is a trifle too hard for me."

120. The Elements of Non-Euclidean Geometry. Preface
A. MS., n.p., n.d., 3 pp., plus 3 pp. which may be part of the same draft.

121. [On Non-Euclidean Geometry]
A. MS., G-undated-6, pp. 2-11; plus 4 pp. of an earlier draft.
Probably manuscript of an address to the New York Mathematical Society, November 24, 1894. Published, in part, as 8.93 n2. Was Euclid a non-Euclidean geometer? Probably! Properties of space. Evidence for thinking there is an absolute which is a real quadric surface. Newton's argument that space is an entity and its bearing on non-Euclidean Geometry. On back of p. 11: "Professor Fiske" [i.e., Thomas S. Fiske].

122. Non-Euclidean Geometry. Sketch of a Synthetic Treatment
A. MS., n.p., n.d., 32 pp. (several attempts with different titles).

123. Lobachevski's Geometry
A. MS., n.p., n.d., 3 pp.

124. Formulae
A. MS., notebook, n.p., n.d.
Notes on non-Euclidean geometry, existential graphs, and Laurent's probabilities. Solution of quadratic equation. The "formulae" of the title refers to trigonometrical formulae and formulae of analytic geometry.

PROJECTIVE GEOMETRY

125. Geometry. Book 1. Projective Geometry
A. MS., n.p., n.d., pp. 1-4.
Definitions: Geometry, Body, Surface, Line, Point.

126. A Geometrico-Logical Discussion
A. MS., n.p., n.d., pp. 1-10, with 28 pp. of other drafts.
Four-ray problem (How many rays cut four given rays?) as offering best apercus into nature of projective geometry. The impossibility of exact ideas, even in mathematics. Idea of a person; idea of a species of animal. Reality and entia rationis. Brief note on verso of one of the pages is dated September 16, 1906, and reads as follows: "11 1/4 P.M. Fell asleep standing and dreamed something about a tablet in a church In memory of my mother."

127. [Fragments on Projective Geometry]
A. MS., n.p., n.d., 61 pp.

128. [Mathematical Notion of Projection]
Amanuensis, with corrections in CSP's hand, n.p., n.d., pp. 11-12.

METRICAL GEOMETRY

129. Metrical Geometry
A. MS., n.p., n.d., pp. 1-39, with variant pages, and 155 pp. of other drafts.
Drafts for MS. 94 or 165. Foundations of linear and angular measurement. Signate, imaginary and quaternional measurement. Concept of a metron. Definitions, theorems, and demonstrations.

130. Metrical Geometry
A. MS., n.p., n.d., 27 pp.
Drafts for MS. 94 or 165. On the nature of spatial measurement.

131. [Metrical Geometry]
A. MS., n.p., n.d., 12 pp.
Drafts for MS. 94 or 165. On propositions holding true for all kinds of systems of measurement.

132. Plan of Geometry
A. MS., n.p., n.d., 28 pp.

133. [Metrical Geometry]
A. MS., n.p., n.d., pp. 1, 14-l5, 17-19
Much of the content, however, is projective geometry which is thought of as requisite for metrics.

134. [Metrical Geometry]
A. MS., n.p., n.d., pp. 27-39, plus 4 pp. of variants.
Drafts for MS. 94 or 165.

135. [Metrical Geometry]
A. MS., n.p., n.d., pp. 56-62, plus a variant p. 58.
Drafts for MS. 94 or 165.

136. [Metrical Geometry]
A. MS., G-undated-12 (Space), 1 p.

TOPICAL GEOMETRY

137. Topical Geometry (Topics)
A. MS., n.p., [1904], pp. 1-29, plus a confusion of partial drafts with pages running as high as p. 40, but with no continuous or final draft.
It is not evident that the title page goes with rest of the manuscript, which was written for Popular Science Monthly. The branches of geometry and their mutual relations. The branches of topics. Topics presupposes time, and time presupposes the doctrine of multitude. The topical properties of time; the hypothetically defined time of topics a true continuum; true continuity opposed to the pseudo-continuity (of the calculus). Instances of time, with the multitude of instances defined with the aid of the secundal system of enumeration. Points as possibilities, not actualized until something occurs to mark them. The dividing point between green and white is both green and white. Law of contradiction does not apply to potentialities. Census Theorem, Census Number, and Listing Numbers. On general words (signs).

138. Analysis of Time
A. MS., notebook, n.p., begun c.1904-05 with two entries dated August 13, 1908.
Four given rays may be crossed by how many rays? The analysis of the Four-ray problem requires a consideration of continuity which in its primitive, i.e., simple, sense has the form of time. Time as a determination of actuality (later see annotation CSP dissents). Definition of terms, e.g., instant, gradations. "I will not take up more of this book with the subject of discrete quantity But I refer to a similar book labelled 'All Pure Quantity merely ordinal' [MS. 224] for more about it."

139. On synectics, otherwise called Topology or Topic
A. MS., n.p., n.d., 4 pp., incomplete.
Synectics as the science of spatial connections; pure synectics as the science of the connection of the parts of true continua.

140. A Treatise on General Topics (General Topics)
A. MS., n.p., n.d., pp. 1-4, plus 1 p., dated December 26, 1913, on what it means to say that a line is continuous.

141. On Topical Geometry, in General (T)
A. MS., G-undated-12, pp. 1-14, 4-8, 4-7, 5-7, 5, 9, 13.
Published, in part, as 7.524-538, except 534n4 and 535n6. Omitted from publication is a discussion of the Kainopythagorean Categories centering in the view that there are but three and that there can be no element in experience not included in the three.

142. Notes on Topical Geometry
A. MS., G-undated-16 [c.1899-1900?], 6 pp., plus 2 pp. each of two other drafts having the same title as above.
Published, in part, as 8.368n23. Omitted from publication are definitions of "thing" and "collection," and a discussion of signs, especially icon, index, and symbol.

143. Topic (Topic)
A. MS., n.p., n.d., pp. 1-4.
Point-figures and line-figures.

144. On General Topic (Topic)
A. MS., n.p., n.d., pp. 1-3, incomplete.
General and special topic distinguished. Properties of a continuum.

*145. An Attempt to state systematically the Doctrine of the Census in Geometrical Topics or Topical Geometry, more commonly called "Topologie" in German books; Being A Mathematical-Logical Recreation of C. S. Peirce following the lead of J. B. Listing's paper in the "G^ttinger Abhandlungen"
A. MS., n.p., n.d., 12 pp.

146. On Space-Logic
A. MS., n.p., November 13, 1895, pp. 1-2 (with a second p. 2), incomplete.
Notation. Topical singularity of a line.

147. On Space-Logic
A. MS., n.p., November 14, 1895, 1 p.
Notation only.

148. Topics of Surfaces
A. MS., n.p., n.d., 1 p.

149. Ch. 2. Topical Geometry
A. MS., n.p., n.d., 1 p.
Definitions of "space," "place," "point," "particle," "line," "filament," "surface," "film," "solid," "body."

150. [Topical Geometry]
A. MS., n.p., n.d., 45 pp.
Draft of MS. 94 or 165. Also material on graphics (projective geometry).

151. Topics. Chapter I. Singular Systems
A. MS., n.p., n.d., 3 pp.
Firstness, or qualities, are positive albeit vague determinations. Vagueness and generality discriminated.

152. Section 4. Of Topical Geometry
A. MS., n.p., n.d., pp. 6-12; 7-8.
Kinds of multitude: numerable, innumerable, enumerable, inenumerable.

153. On the Problem of Coloring a Map (4 Colors)
A. MS., n.p., n.d., pp. 1-17, plus variants.

154. On the Problem of Map-Coloring and on Geometrical Topics, in General (MC, PMC, Map)
A. MS., n.p., [1899-1900], pp. 1-10, plus variants and many other attempts (82 pp. in all), none going beyond p. 10.
The problem of map-coloring is stated as follows: "To determine demonstratively the smallest number of colors that will suffice so as to color any map whatever which can be drawn on a given surface, that no two confine regions (that is, two regions having a common boundary-line) shall have the same color." See CSP W. E. Story correspondence, 12/29/00.

155. Studies in map Coloring as Starting-point for Advance into Geomet-rical Topics
A. MS., notebook, n.p., [c.1897-1900?].
The first part of the notebook, the date of which is c.1870, deals with physical constants.

156. Map Coloring Vol. IV
A. MS., small notebook, n.p., n.d., plus another notebook ("Map Coloring Vol. V"), n.p., n.d.
Study of the Census Number.

157. [Link Coloring]
A. MS., n.p., [c.1897-1900?], 16 pp.
In how many ways, with c colors, can a simple chain of 1 links be colored, no two adjacent links being colored alike? In how may ways, with c + l colors, can a simple chain of I + l links be colored so that all adjacent links are colored differently?

158. [Fragments on Map-Coloring]
A. MS., n.p., n.d., 32 pp. and 3 pp.

159. Notes on Listing
A. MS., n.p., [1897?], pp. 1-7.

160. A Study of Listing Numbers (Listing Numbers)
A. MS., n.p., February 3, 1897, pp. 1-5, plus 1 p. which apparently belongs here.

161. [Listing Numbers; The Census-Number; The Census Theorem]
A. MS., n.p., n.d., 5 pp.

162. [Fragments on Listing Numbers and the Census-Number]
A. MS., n.p., n.d., 8 pp.

163. [Topology; Real Curves; Astronomy; Archeology; Assorted Mathematical Notes]
A. MS., notebook, n.p., 1895 (p. 45 is dated July 1895).

MATHEMATICAL TEXTBOOKS

164. New Elements of Mathematics
A. MS., n.p., [c.1895], title page and 2 pp. ("Preface").
An introduction to a book which is designed to give the educated man all the mathematics he needs to know and which could serve as preparation for the study of higher mathematics. Brief account of the recent history of mathematics, followed by an examination of the branches of geometry.

165. Elements of Mathematics
A. MS., n.p., [c.1895], pp. 1-357 (pp. 61, 77, 93, 213, 259-273, 276-294 missing), with 23 pp. of a well-detailed "Table of Contents" and "Subject Index" and 18 pp. of another draft of Article 2, Scholium 2, of Chapter I.
Chapter I "Introduction" (pp. 1-39): Elementary account of the nature of mathematics; analysis of the game of tit-tat-too as an illustration of the process of deducing the consequences of hypotheses; definitions and the etymology of important terms. See MS. 1525 for possible early drafts of some of this material. Chapter II "Sequences" (pp. 40-76, with p. 61 missing): Sequences, both simple and complex. Chapter III "The Fundamental Operations in Algebra" (pp. 78-92, with pp. 77 and 93 missing): Fundamental operations in algebra; explicit and implicit functions; functions of several variables. Chapter IV "Factors" (pp. 94-106): Parts, divisors, and factors; prime factors; greatest common divisor of several numbers; multiples, dividends, and products; least common multiple; fundamental theorem of composition. Chapter V "Negative Numbers" (pp. 107 116): Definition and historical data. Chapter VI "Fractional Quantities" (pp. 117-130): Rational number explained; the system of rational numbers as including the values of all rational fractions except o/o. Chapter VII "Simple Equations" (pp. 131-173): Solution of linear equations; systems of simultaneous equations. Chapter VIII "Ratios and Proportions" (pp. 174-188): Ratios, proportions, anharmonic ratio. Chapter IX "Surds" (pp. 189-222, with p. 213 missing): Possibility and importance of surds; definition of "limit"; Achilles and the tortoise (p. 196); imaginary quantities; exercises and problems. Chapter X "Topical Geometry" (pp. 223-275, with pp. 259-273, 276-293 missing): Topical geometry explained; continuum; homo-geneity; tridimensionality of space; singularities; topical classes of surfaces; the topical census. Long footnote on the intelligibility of infinitesimals. Chapter XI "Perspective" (pp. 294-357): Graphics; homoloidal system of plates; dominant (optical) homoloids; projection; Desarques' Ten-Line theorem; the Nine-Ray theorem.

166. Elements of Mathematics
A. MS., n.p., [c.1895], pp. 44-320, with many gaps and variant pages.
Another draft of MS. 165.

167. Practical Arithmetic

A. MS., n.p., n.d., pp. 1-29 (pp. 26-27 missing), plus 2 pp.
Maxims for attaining accuracy and speed in handling numbers. Counting and measuring. The decimal names of numbers. The arabic notation.

168. Practical Arithmetic
TS. (corrected), n.p., n.d., 21 pp. of two drafts.

169. Factotal Augrim (A) (B)
A. MS., n.p., n.d., pp. 1-18 (A), 5-18 (A), plus variants; 1-4 (B).
Terminology: augrim, arithmetic, vulgar arithmetic, practical arithmetic, ciphering, and algorithm. Elementary and composite augrims. On number, including a long footnote on collections.

170. Rough List of Works Consulted for Arithmetic
A. MS., n.p., [1890-91?], 3 pp.

171. CSP's Small Inventions in Arithmetic and Logic
A. MS., n.p., n.d., 8 pp.
The arrangement of all the rational fractions, not negative, in the order of their values and without calculation.

172. Examples in Arithmetic
A. MS., n.p., n.d., 8 pp.

173. A System of Arithmetic
A. MS., n.p., n.d., 3 pp.
Rule for addition.

174. Rule for Division
A. MS., n.p., n.d., pp. 1-28 (pp. 2, 13, 15-16, 23-26 missing), plus variants and several unnumbered pages.

175. Exercises in Arithmetic
A. MS., notebook, n.p., n.d.

176. [Elementary Arithmetic]
A. MS., n.p., n.d., 15 pp.
Rule for addition. Counting by threes, fours, fives, etc.

177. The Practice of Vulgar Arithmetic
A. MS., notebook, n.p., n.d.
Addition, multiplication, squaring a number, solving algebraic equations, Rule of False.

178. C. S. Peirce's Vulgar Arithmetic: Its Chief Features
A. MS., notebook, n.p., [c.1890].
Draft of a book, outlining its chief features. Shortcuts in the teaching of arithmetic.

179. Peirce's Primary Arithmetic Upon the Psychological Method
A. MS., n.p-, [1893], 52 pp.
Teaching numeration. Addition. Multiplication.

180. Plan of the Primary Arithmetic
A. MS., n.p., n.d., pp. 1-3.
The contents of seventeen chapters are noted.

181. Primary Arithmetic
A. MS., n.p., n.d., 31 pp.
Six lessons concerned with counting.

182. Primary Arithmetic. Suggestions to Teachers
A. MS., n.p., n.d., 12 pp.
A teaching manual on counting.

183. Mugling Arithmetic
A. MS., n.p., n.d., pp. 1-2.

184. [On Counting]
A. MS., n.p., n.d., 4 pp.

185. Chapter IV. Addition
A. MS., n.p., n.d., 6 pp.

186. Familiar Letters about the Art of Reasoning
A. MS., n.p., May 15, 1890, pp. 1-22, plus title page and 2 pp. (unnumbered).
In the form of a letter to Barbara (of the mnemonical verses). Card-playing as a pedagogical instrument, useful in teaching the art of reasoning.

187. [Assorted Notes for an Elementary Arithmetic]
A. MS., n.p., n.d., 6 pp. (not all in CSP's hand).

188. [Introduction to Practical Arithmetic]
A. MS., n.p., n.d., 2 pp.
Discussion is somewhat advanced and may not be part of a primary or vulgar arithmetic.

189. Lydia's Peirce's Primary Arithmetic
A. MS., notebook, n.p., [1904-05], with 65 pp. of drafts.
"Grandmother" Lydia teaches counting, making use of children's nonsense rhymes like "eeny-meeny-mony-meye," but pointing up the numerical limitations of gibberish.

190. [Notes on Square Roots, Long Division, Addition, Cyclic Numeration]
A. MS., n.p., n.d., 9 pp.

191. [Balance and Scales]
A. MS., n.p., n.d., 13 pp.
Part of a proposed book for children.

192. [On Algebra]
A. MS., n.p., n.d., pp. 2-15.
An elementary discussion possibly for a textbook.

193. Syllabus of the Elements of Trigonometry
A. MS., n.p., n.d., 4 pp., representing three different starts.

194. [Fragments on Trigonometry]
A. MS., n.p., n.d., over 100 pp.

195. Trigonometry
A. MS., n.p., n.d., pp. 1-2, plus 13 pp.

196. Sketch of a Proposed Treatise on Trigonometry
A. MS., n.p., n.d., 20 pp.

197. Elements of Geometry
A. MS., n.p., n.d., 1 p.

198. [Geometry Exercises]
A. MS., n.p., n.d., 14 pp.

MATHEMATICAL RECREATIONS

199. The Third Curiosity (MM/D)
A. MS., n.p., [1907], pp. 1-76, plus 53 rejected pages.
Numeration with a base other than 10. Sextal and secundal systems. The rules of arithmetic, e.g., rule of algebraic summation and the rule of "direct division."

200. The Fourth Curiosity (MM/E)
A. MS., G-1908-1e, pp. 1-186, plus 161 pp. (running brokenly to p. 186).
Omitted from publication in the Collected Papers: further discussion of the relationships of the Aristotelian pattern; definition of "pure mathematics"; numbers as entia rationis; first valid argument for pragmatism involves the denial of the Absolute. Kind, class, and collection. Signs and predication.

201. A Contribution to the Amazes of Mathematics (MM)
A. MS., n.p., [c.1908], 210 pp., most of which are numbered with the numbered pages running as high as p. 164 (many pages missing, however).
Rationale for two card "tricks" [The First (?) and Second Curiosities]. Abstract real (not imaginary) numbers viewed pragmatistically. Cantorian system. Cyclical system of numbers. The Fourth Curiosity. Secundal arithmetic. Reference to Elements of Mathematics (MS. 165), with bitter note on publishers of textbooks.

202. Some Amazements of Mathematics (Cu)
A. MS., n.p., [c.1908], pp. 1-53, plus 26 pp. of variants.
This paper begins with an analysis of the peculiarity of the number 142857. Lengthy discussion of infinitesimals. Fermat's theorem, Polynomial theorem, Rule of "direct division." Card "trick" (same as one of the two card "tricks" of MS. 201).

203. Addition (Add)
A. MS., n.p., May 24, 1908, pp. 1-5.
Alternate draft of 4.642. Does the collective system of irrational and rational quantity constitute a continuum or a pseudo-continuum? CSP says "pseudo-continuum" as against the opinions of both Cantor and Dedekind.

204. Supplement (A)
A. MS., G-1908-1b, pp. 1-17, incomplete, with variants.
The exact date of this manuscript is May 24, 1908. It was published, in part, as 7.535n6. Unpublished: Whether mathematicians generally, including Cantor and Dedekind, are correct in their views as to what constitutes a true continuum. The three universes of ideas, i.e., arbitrary possibilities, physical things, and minds. Reality and existence; perfect and imperfect continua.

205. Recreations in Reasoning (RR)
A. MS., G-c.1897-4, pp. 1-35, plus 22 pp. probably from another draft.
Published as 4.153-169, with the proofs of several theorems omitted.

206. Recreative Exercises in Reasoning (R)
A. MS., n.p., n.d., pp. 1-4.
Solution of the following exercise: "Required to arrange all the rational fractions (whose denominators do not exceed a given number and whose numerators do not exceed a given number of times the denominator) in the order of their values, in a horizontal row with < or = interposed between each successive two to state their relation of value."

207. Recreations in Reasoning (R)
A. MS., n.p., n.d., pp. 1-24, 2-5 with one rejected page and 14 pp. of variants; plus 11 pp. of notes.
Three distinguishing marks of numerical multitude. The ordering of fractions and the simplest method for calculating circulating decimals.

208. Recreations of Reasoning (RR)
A. MS., n.p., [c.1897], pp. 1, 21, 32; and 1 p.

209. Knotty Points in the Doctrine of Chances
A. MS., n.p., [c.1899], pp. 1-16.
Problem in probabilities: mathematics of the roulette table. CSP concludes whimsically: "That in an even game, say an honest roulette without zeros, all the players might make it a rule to leave off only when they had netted a winning equal to a single bet, and were their fortunes or backing unlimited, every man of them would be sure of success, while the bank, though it would not win anything, would never lose!" Now "let U.S. lend to each citizen ..." and then allow the winnings to be taxed.

210. A Corner for Pythagoreans. Mathematical Recreations No. 1 by Pico di Sablonieri (pseudonym)
A. MS., n.p., [c.1895], pp. 1-11; plus 12 pp. and 5 pp. of other drafts.
A problem in probabilities. Content is similar to that of the preceding manuscript.

211. A Brief Preliminary and Hasty Syllabus of a book to be entitled Calculations of Chances
A. MS., n.p., n.d., 38 pp.; plus pp. 8, 11-18.

COMPUTATIONS AND FRAGMENTS

212. A Trade Secret (Trade Secret)
A. MS., n.p., n.d., pp. 1-4, with a variant p. 1.
The computing of values of a function from an infinite series: a dodge generally known among professional computers.

213. Notes of a Computer
A. MS., n.p., n.d., pp. 1-3, plus 1 p. ("A Device of Computation") and 1 p. ("A Computer's Device").

214. Note on o(inf)
TS., n.p., n.d., 3 pp.

215. Integer Negative Powers of 2
A. MS., n.p., "checked and found correct by CSP 1911, Oct. 8," 2 pp.

216. Practical Comments on Namur's Tables of Logarithms
A. MS., n.p., n.d., 1 p.

217. Calc. of Nat. Log. 10
A. MS., n.p., n.d., 1 sheet.

218. A Short Table of Reciprocals
A. MS., n.p., n.d., 1 sheet.

219. Computation of the excess of 5/10 over 1
A. MS., n.p., n.d., 1 p.

220. Calculation of the fractional part of 5/10
A. MS., n.p., n.d., 2 pp.

221. Hints toward the invention of a Scale-Table
A. MS., n.p., n.d., pp. 1-6; 1-3; and 9 pp. of fragments.
Table of antilogarithms and a logarithmic scale.

222. Dedekind's Dirichlet #23
A. MS., n.p., n.d., pp. 1-3, plus 5 pp. of two other starts.
The object of this paper is to describe a notation which reveals clearly the elementary constitution and properties of the functions connected with the GCD algorithm.

223. Gibb's Papers. Vol. II. p. 30
A. MS., n.p., n.d., 3 pp.
Probably a draft of G-1883-5d.

224. All Pure Quantity merely ordinal
A. MS., notebook, August 16, 1908.
Notes for a memoir whose purpose is "to prove that every system of signs of abstract quantities signifies nothing but that one sign denotes an object later in one or more sequences (or later in one and earlier in another, etc.) than an object denoted by another." A study of two systems: (a) additive scheme of rational values, (b) numerative scheme of positive fractions. Ens rationis and feeling (monadic experience contrasted with dyadic experience, or "reaction").

225. Memorandum of How to Do Things
A. MS., notebook, n.p., n.d.
Various formulae of computation. Certain kinds of problems, e.g., drawing the best algebraic curve of a given order through any number of points, finding times of moon's rising and setting, etc., and their solutions.

226. Note to p. 378 of [Benjamin] Peirce's Analytic Mechanics
A. MS., n.p., n.d., 4 pp.

227. Theorems of Numbers
A. MS., n.p., n.d., 2 pp., incomplete.

228. Notes
A. MS., n.p., n.d., 9 pp.
Distributions of the theorems of mathematics throughout the various branches of the discipline. In addition, the notes are concerned with the theory of equations, equal roots, symmetric functions, different kinds of ratios.

229. [Logic of Number] (Lefevre)
A. MS., n.p., n.d., pp. 2-7, 16, 18, 20-21.
Definition of "mathematics" as "the science of hypotheses."

230. [Analytic Geometry]
A. MS., notebook, n.p., n.d.
Includes, in addition to the material on analytic geometry, a personal expense account, covering several days, but with no indication of the year.

231. Studies of Laws of Frequency of Occurrence of Numbers
A. MS., n.p., n.d., 1 p.
These studies are based on population figures for 1900.

232. Note on the Mouse Trap Problem
A. MS., n.p., n.d., 1 p.

233. Gauss's Rule for Easter improved
A. MS., n.p., n.d., 1 p.

234. [Arithmetical Calculations]
A. MS., notebook, n.p., n.d.

235. [Fragment on Quantity]
A. MS., n.p., n.d., pp. 15-16.

236. [Fermat's Theorem]
A. MS., n.p., n.d., 4 pp.
Draft of a postscript to an unidentified letter.

237. Formulae for Repeated Differentiations (Repeated Differentiations)
A. MS., n.p., n.d., pp. 1-2; plus 2 pp. (Dn).

238. An Apology for the Method of Infinitesimals (Apology)
A. MS., n.p., n.d., pp. 1-15.
An attempt at justifying a remark (see Century Dictionary s.v. limit) that the method of infinitesimals is more in harmony with advances in mathematics (1883) than the method of limits.

239. Infinitesimals
Corrected proofs, G-1900-1.

240. A Mathematical Suggestion
A. MS., n.p., n.d., 1 folded sheet (4 pp.).

241. A Mathematical Discussion
A. MS., n.p., n.d., l folded sheet (4 pp.).

242. [Computation of Ordinates for Points on a Probability Curve]
A. MS., n.p., n.d., 1 p.

243. The Theta Function of Probabilities
A. MS., n.p., n.d., 1 p., with 5 sheets of calculations.

* 244. [A Problem in Probabilities]
A. MS., notebook, n.p., n.d.
Solution of algebraic problems. Venn Diagrams. Calculation of the asymptotic axis of the larger atomic weights.

245. Illustrative Problem in Probabilities
A. MS., n.p., n.d., 16 pp.

246. Reflections on the Logic of Science
A. MS., n.p., January 1-7, 1889, pp. 2-22
Evidently for a book on the philosophy of physics. The relationship between mathematics and physical theory. The Rule of False. MSS. 247-249 are presumably continuations of this one.

247. Chapter II. The Doctrine of Chances
A. MS., n.p., January 8, 1889, pp. 23-29, plus another p. 27.

248. Chapter II. Mathematics
A. MS., n.p., January 9-17, 1889, pp. 23-29.

249. Ordinal Geometry
A. MS., n.p., January 18-19, 1889, 40 pp., representing several starts.

250. Notes for Chapter of Mathematics
A. MS., n.p., November 24-25, 1901, pp. 1-4.

251. Topics of Mathematics
A. MS., n.p., n.d., 1 p.

252. [On Mathematical Reasoning]
A. MS., n.p., n.d., 22 pp.
Mathematical reasoning illustrated by means of the game tit-tat-too. The advantage, in general, of studying mathematics.

253. Logical Analysis of Some Demonstrations in High Arithmetic (D)
A. MS., n.p., June 11, 1905, pp. 1-20, incomplete, with an alternate p. 20.
Reference is made to a paper published in The American Journal of Mathematics (G-1881-7). Demonstrations of Fermat's and Wilson's theorems.

254. Of the Nature of Measurement
A. MS., G-undated-4, pp. 1-26, plus 6 pp. rejected.
Published, in part, as 7.280-312. Omitted are the demonstration and scholium in connection with the theorem on hyperbolic motion (pp. 13-17) and the corollary of the definition occurring on p. 21 and published as 7.312 (pp. 22-26).

255. Of the Nature of Measurement
A. MS., n.p., n.d., pp. 1-8, plus variants.

256. Properties of Space
A. MS., n.p., n.d., 11 pp. (fragmentary).

257. [On the Properties of Space]
A. MS., n.p., n.d., 6 pp. and 5 pp. of another draft.
The three classes of spatial properties: intrinsic, metrical, and optical.

258. [On the Properties of Mathematical Space]
A. MS., n.p., n.d., 2 pp.
Space is tri-dimensional and unlimited; its points are continuous; and it has the same properties everywhere, and in all directions.

259. Note on the Analytic Representation of Space as a Section of a Higher Dimensional Space
A. MS., n.p., n.d., 1 p.

260. Note on the Utility of considering Space as a Section of a Space of more than 3 Dimensions
A. MS., n.p., n.d., 4 pp.

261. Notes on Geometry of Plane Curves without Imaginaries
A. MS., n.p., n.d., pp. 1-5, plus 6 pp.

262. On the Real Qualitative Characters of Plane Curves
TS., n.p., n.d., 12 pp. of several drafts.

*263. Singularities of Pairs of Terminals
A. MS., n.p., n.d., 2 pp.

264. On the Real Singularities of Plane Curves
A. MS., n.p., n.d., 9 pp.

265. Topical Singularities
A. M.S., n.p., n.d., 3 pp.

266. [Worksheets on the Nine-Ray Theorem]
A. MS., notebook, n.p., n.d.

267. [Points, Lines, and Surfaces]
A. MS., notebook, n.p., n.d.

268. Euclid Easy. Chapter I. A Talk on Continuity
A. MS., n.p., n.d., pp. 1-4.
An imaginary conversation between Thomas J. Jeffers and Euclid Easy, preparatory to a full scale discussion of the logic of continuity.

269. Notes for Theorems
A. MS., notebook, n.p., n.d.
Various topics are listed with reference both to standard works and other writings. Topology and the four-color problem.

270. Test-Example of Mathematical Reasoning
A. MS., n.p., n.d., 6 pp.
An inquiry which presupposes points, rays, planes, and a relation called "containing."

271. Pythagorean
A. MS., n.p., n.d., 1 p.

272. Remarkable points of a triangle
A. MS., n.p., n.d., 2 pp., and 4 pp. ("Triangle").

273. [Homoloids]
A. MS., n.p., n.d., 8 pp.
Discussion of the four-ray problem.

274. The Dodecanes
A. MS., n.p., n.d., 26 pp,

275. On a Geometrical Notation
TS., n.p., n.d., 2 pp., with 2 pp. of TS. (corrected) on "Notation."

276. Miscellaneous Journal
A. MS., notebook, dated entries for February 9, 11, 14-15, 20, 25, 28, 1910.
Secundal arithmetic. Probability. Petersburg problem. Justification for asserting a proposition. Analysis of the predicate "positive." Also a draft of a letter apparently to Mrs. O. H. P. Belmont.

277. The Prescott Book
A. MS., n.p., begun May 1907 and continued June 8, 1907-September 13, 1910.
On singularities, Petersburg problem, Ten-Point theorem, continuity, existential graphs. An analysis of signs, notes on phaneroscopy, and an outline of a paper for the Hibbert Journal on "a little known 'Argument' for the Being of God."

*278. [Unidentified Fragments]
A. MS., n.p., n.d., over 1400 pp.